Trigonometry · JEE Main previous year questions

2012 5 questions

1. Q62012 · 26 May 2012 · Shift 1

   The value of $\cos 255^{\circ }+\sin 195^{\circ }$ is

   1. A.$\frac{\sqrt{3}-1}{2\sqrt{2}}$
   2. B.$\frac{\sqrt{3}-1}{\sqrt{2}}$
   3. C.$-\frac{\sqrt{3}-1}{\sqrt{2}}$
   4. D.$\frac{\sqrt{3}+1}{\sqrt{2}}$
   Show answer

   Answer: C

2. Q162012 · 26 May 2012 · Shift 1

   $f(x)=\int \frac{dx}{{\sin }^{6}x}$ is a polynomial of degree

   1. A.$5\text{ in }\cot x$
   2. B.$5\text{ in }\tan x$
   3. C.$3\text{ in }\tan x$
   4. D.$3\text{ in }\cot x$
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   Answer: A

3. Q132012 · 12 May 2012 · Shift 1

   If $f^{\prime }(x)=\sin (\log x)$ and $y=f\left(\frac{2x+3}{3-2x}\right)$, then $\frac{dy}{dx}$ equals

   1. A.$\sin \left[\log \left(\frac{2x+3}{3-2x}\right)\right]$
   2. B.$\frac{12}{(3-2x{)}^2}$
   3. C.$\frac{12}{(3-2x{)}^2}\sin \left[\log \left(\frac{2x+3}{3-2x}\right)\right]$
   4. D.$\frac{12}{(3-2x{)}^2}\cos \left[\log \left(\frac{2x+3}{3-2x}\right)\right]$
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   Answer: C

4. Q262012 · 12 May 2012 · Shift 1

   If in a triangle $ABC$, $\frac{b+c}{11}=\frac{c+a}{12}=\frac{a+b}{13}$, then $\cos A$ is equal to

   1. A.$5/7$
   2. B.$1/5$
   3. C.$35/19$
   4. D.$19/35$
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   Answer: B

5. Q202012 · 7 May 2012 · Shift 1

   Let $y(x)$ be a solution of $\frac{2+\sin x}{1+y}\frac{dy}{dx}=\cos x$. If $y(0)=2$, then $y\left(\frac{\pi }{2}\right)$ equals

   1. A.$\frac{5}{2}$
   2. B.2
   3. C.$\frac{7}{2}$
   4. D.3
   Show answer

   Answer: C